Question 1

LESSON 1:
Function Notation

Accepted Answer

a relation in which every input results in one and only one output; usually denoted with f(x), g(x), h(x), k(x)  and other letters

Question 2

Radical Function:

Accepted Answer

f(x)= √x

Question 3

Radicand

Accepted Answer

the value under the square root

Question 4

Rational Function

Accepted Answer

f(x)= 1/x

Question 5

Domain (inputs)

Accepted Answer

all possible inputs (x-values) of a function; values that are independent in an equation or expression

Question 6

Denominator Restriction

Accepted Answer

domain values that render a rational expression undefined.

Question 7

Square Root (even root) Restriction

Accepted Answer

domain values that render a square root expression undefined

Question 8

Range (outputs)

Accepted Answer

all possible outcomes (y-values) of a function; values that are dependent in an equation or expression

Question 9

Interval Notation

Accepted Answer

A way to indicate inequalities by using brackets or parenthesis instead of inequality system.

Question 10

U (union)

Accepted Answer

Symbol used to merge 2 or more pieces of an interval

Question 11

Point of Discontinuity

Accepted Answer

an x-value on the graph where the y-value is undefined

Question 12

Continuous Graph

Accepted Answer

a graph with a domain of (-∞, ∞)

Question 13

Discontinuous Graph

Accepted Answer

a graph with a domain OTHER THAN (-∞, ∞)

Question 14

Vertical Asymptote

Accepted Answer

domain values that render a rational expression undefined

Question 15

Horizontal Asymptote

Accepted Answer

range values that render a rational expression undefined

Question 16

LESSON 2:
Vertical Stretch/Shrink

Accepted Answer

occurs when a function is multiplied by a constant, a.  If a is between 0 and 1, there is a vertical shrink (or compression).  If a is greater than 1, there is a vertical stretch. Both by a factor of a.

Question 17

Horizontal Stretch/Shrink

Accepted Answer

Occurs when a  function's input is multiplied by a constant, b.  If b is between 0 and 1, there is a horizontal stretch by a factor of 1/b.  If b is greater than 1, there is a horizontal shrink (or compression) by a factor of 1/b.

Question 18

Horizontal Translation left/right

Accepted Answer

occurs when a constant is added to or subtracted from a function's input.  Adding a constant = translation left; Subtracting a constant = translation right.

Question 19

Horizontal Translation Up/Down

Accepted Answer

occurs when a constant is added to or subtracted from a function.  Adding = translation up; Subtracting = translation down.

Question 20

Vertical Translation Up/Down

Accepted Answer

occurs when a constant is added to or subtracted from a function.  Adding = translation up; Subtracting = translation down.

Question 21

Reflection Over X-Axis

Accepted Answer

occurs when a function is multiplied by a negative coefficient.

Question 22

Reflection Over Y-Axis

Accepted Answer

Occurs when a function's INPUT is multiplied by a negative coefficient.

Question 23

LESSON 3:
Rigid Transformation

Accepted Answer

a transformation that does NOT alter the size or shape of a function

Question 24

Nonrigid Transformation

Accepted Answer

a transformation that does alter the size or shape of a graph (e.g., dilation)

Question 25

LESSON 4 AND 5:
Piecewise Functions

Accepted Answer

a function made up of multiple sub-equations, where each sub-function applies to a different interval in the domain

Question 26

Evaluate

Accepted Answer

finding the output value of a function f(x) that corresponds to a given input value, x.

Question 27

Vertical Line Test

Accepted Answer

a visual method used to determine whether a given curve is a function or not

Question 28

LESSON 6:
Increasing

Accepted Answer

an interval in which the y-value increases as the x-value increases.

Question 29

Decreasing

Accepted Answer

an interval in which the y-value decreases as the x-value increases.

Question 30

Boundedness

Accepted Answer

the limits or bounds of a function.

Question 31

Bounded Above

Accepted Answer

a function is bounded above by the number A if the number A is higher than or equal to all values of the function

Question 32

Bounded Below

Accepted Answer

a function is bounded below  by the number B if the number B is lower than or equal to all values of the function

Question 33

Bounded

Accepted Answer

a function that is bounded both above and below

Question 34

Unbounded

Accepted Answer

a function that is neither bounded above nor below

Question 35

Bounded on an Interval

Accepted Answer

an interval is bounded when both its endpoints are included in the domain

Question 36

Extrema

Accepted Answer

a point at which a maximum or minimum value of the function is obtained in some interval

Question 37

Local(relative)

Accepted Answer

the point is a max or min relative to the points around it

Question 38

Absolute

Accepted Answer

the highest or lowest point in the entire domain

Question 39

Maximum

Accepted Answer

the largest y-value of a function over a set domain; the point where the function changes from increasing to decreasing

Question 40

Minimum

Accepted Answer

the smallest y-value of a function over a set domain; the point where the function changes from decreasing to increasing

Question 41

LESSON 8:
Composition of Functions

Accepted Answer

a function made of other functions, where the output of one function is the input of another function	
(f∘g)(x)=f(g(x)): "f of g", indicates that g(x) is the input to f(x).

Question 42

Not Commutative

Accepted Answer

the property that order DOES matter when composing

Question 43

Restricted Domain

Accepted Answer

a domain for a function that is smaller than the function's domain of definition; typically used to specify a one-to-one section of a function

Question 44

Decomposition

Accepted Answer

breaking a given composed equation into the inner and outer function

Question 45

LESSON 9:
Inverse Relation

Accepted Answer

a set of ordered pairs obtained by interchanging the first and second coordinates of each pair in the original function

Question 46

Horizontal Line Test

Accepted Answer

a test consisting of drawing horizontal lines through a function to prove whether it is one-to-one and therefore has an inverse that is also a function.

Question 47

One-to-One

Accepted Answer

any output value, y, in a function has exactly one input, x.  If a function is one-to-one, then it has an inverse that is also a function.

Question 48

Inverse Function

Accepted Answer

a function that undoes the action of another function.  A function g is the inverse of a function f if y=f(x) then x=g(y).
		5. f^(−1) (x):"f inverse"

Question 49

Inverse Reflection Principle

Accepted Answer

a function and its inverse will be reflections of each other over the line y=x.

Question 50

Inverse Composition Rule

Accepted Answer

when f and g are inverse, the composition of f and g (in either order) creates a function that for every input returns the input: f(g(x))=g(f(x))=x.
		*** When composing two inverse functions fand f^(−1), f(f^(−1) (x))=f^(−1) (f(x))=x.

Term	Definition
LESSON 1: Function Notation	a relation in which every input results in one and only one output; usually denoted with f(x), g(x), h(x), k(x) and other letters
Radical Function:	f(x)= √x
Radicand	the value under the square root
Rational Function	f(x)= 1/x
Domain (inputs)	all possible inputs (x-values) of a function; values that are independent in an equation or expression
Denominator Restriction	domain values that render a rational expression undefined.
Square Root (even root) Restriction	domain values that render a square root expression undefined
Range (outputs)	all possible outcomes (y-values) of a function; values that are dependent in an equation or expression
Interval Notation	A way to indicate inequalities by using brackets or parenthesis instead of inequality system.
U (union)	Symbol used to merge 2 or more pieces of an interval
Point of Discontinuity	an x-value on the graph where the y-value is undefined
Continuous Graph	a graph with a domain of (-∞, ∞)
Discontinuous Graph	a graph with a domain OTHER THAN (-∞, ∞)
Vertical Asymptote	domain values that render a rational expression undefined
Horizontal Asymptote	range values that render a rational expression undefined
LESSON 2: Vertical Stretch/Shrink	occurs when a function is multiplied by a constant, a. If a is between 0 and 1, there is a vertical shrink (or compression). If a is greater than 1, there is a vertical stretch. Both by a factor of a.
Horizontal Stretch/Shrink	Occurs when a function's input is multiplied by a constant, b. If b is between 0 and 1, there is a horizontal stretch by a factor of 1/b. If b is greater than 1, there is a horizontal shrink (or compression) by a factor of 1/b.
Horizontal Translation left/right	occurs when a constant is added to or subtracted from a function's input. Adding a constant = translation left; Subtracting a constant = translation right.
Horizontal Translation Up/Down	occurs when a constant is added to or subtracted from a function. Adding = translation up; Subtracting = translation down.
Vertical Translation Up/Down	occurs when a constant is added to or subtracted from a function. Adding = translation up; Subtracting = translation down.
Reflection Over X-Axis	occurs when a function is multiplied by a negative coefficient.
Reflection Over Y-Axis	Occurs when a function's INPUT is multiplied by a negative coefficient.
LESSON 3: Rigid Transformation	a transformation that does NOT alter the size or shape of a function
Nonrigid Transformation	a transformation that does alter the size or shape of a graph (e.g., dilation)
LESSON 4 AND 5: Piecewise Functions	a function made up of multiple sub-equations, where each sub-function applies to a different interval in the domain
Evaluate	finding the output value of a function f(x) that corresponds to a given input value, x.
Vertical Line Test	a visual method used to determine whether a given curve is a function or not
LESSON 6: Increasing	an interval in which the y-value increases as the x-value increases.
Decreasing	an interval in which the y-value decreases as the x-value increases.
Boundedness	the limits or bounds of a function.
Bounded Above	a function is bounded above by the number A if the number A is higher than or equal to all values of the function
Bounded Below	a function is bounded below by the number B if the number B is lower than or equal to all values of the function
Bounded	a function that is bounded both above and below
Unbounded	a function that is neither bounded above nor below
Bounded on an Interval	an interval is bounded when both its endpoints are included in the domain
Extrema	a point at which a maximum or minimum value of the function is obtained in some interval
Local(relative)	the point is a max or min relative to the points around it
Absolute	the highest or lowest point in the entire domain
Maximum	the largest y-value of a function over a set domain; the point where the function changes from increasing to decreasing
Minimum	the smallest y-value of a function over a set domain; the point where the function changes from decreasing to increasing
LESSON 8: Composition of Functions	a function made of other functions, where the output of one function is the input of another function (f∘g)(x)=f(g(x)): "f of g", indicates that g(x) is the input to f(x).
Not Commutative	the property that order DOES matter when composing
Restricted Domain	a domain for a function that is smaller than the function's domain of definition; typically used to specify a one-to-one section of a function
Decomposition	breaking a given composed equation into the inner and outer function
LESSON 9: Inverse Relation	a set of ordered pairs obtained by interchanging the first and second coordinates of each pair in the original function
Horizontal Line Test	a test consisting of drawing horizontal lines through a function to prove whether it is one-to-one and therefore has an inverse that is also a function.
One-to-One	any output value, y, in a function has exactly one input, x. If a function is one-to-one, then it has an inverse that is also a function.
Inverse Function	a function that undoes the action of another function. A function g is the inverse of a function f if y=f(x) then x=g(y). 5. f^(−1) (x):"f inverse"
Inverse Reflection Principle	a function and its inverse will be reflections of each other over the line y=x.
Inverse Composition Rule	when f and g are inverse, the composition of f and g (in either order) creates a function that for every input returns the input: f(g(x))=g(f(x))=x. *** When composing two inverse functions fand f^(−1), f(f^(−1) (x))=f^(−1) (f(x))=x.

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Unit 1 Vocab Pre Cal